Theory and Decision

, Volume 52, Issue 4, pp 303–312

Semicontinuous Representability of Homothetic Interval Orders by Means of Two Homogeneous Functionals

Authors

  • Gianni Bosi
    • Dipartimento di Matematica Applicata `Bruno de Finetti'Università di Trieste
Article

DOI: 10.1023/A:1020298220758

Cite this article as:
Bosi, G. Theory and Decision (2002) 52: 303. doi:10.1023/A:1020298220758

Abstract

It is well known that interval orders are particularly interesting in decision theory, since they are reflexive, complete and nontransitive binary relations which may be fully represented by means of two real-valued functions. In this paper, we discuss the existence of a pair of nonnegative, positively homogeneous and semicontinuous real-valued functionals representing an interval order on a real cone in a topological vector space. We recover as a particular case a result concerning the existence of a nonnegative, positively homogeneous and continuous utility functional for a complete preorder on a real cone in a topological vector space.

Interval orderTopological vector spaceUtility function

Copyright information

© Kluwer Academic Publishers 2002